The role of the teacher in fostering students’ evolution across different layers of generalization by means of argumentation

Resumen

We address students’ processes of generalization in early algebra and investigate how the teacher can support them in developing interpretations of non-canonical arithmetic representations, by means of argumentation. Data are constituted by grade 5 students written protocols and excerpts from video-recorded classroom discussions. The analysis is developed on qualitative base, referring to three main aspects: the layers of generalization that emerge in students’ semiotic activities, the argumentation, with reference to the criteria of correctness, clearness, and completeness, and the roles played by the teacher to foster students’ generalization and argumentation processes. Results point out three specific roles that revealed powerful for fostering students’ evolution across different layers of generalization, by means of argumentation: reflective guide, activator of reflective attitudes and activator of interpretative processes.